Randomised Portfolios in Insurance

Introduction

Basic Concept


Insurance Use Cases

Random Portfolios

Risk/Reward Tradeoff


Risk Tolerance

Risk Limits


Only NASDAQ, NYSE listed stocks


No single stock greater than 5% of portfolio


Market Cap greater than 100M USD


No sector greater than 25% of portfolio

Key Finding


Portfolio performance is highly dependent on risk limits

Separate “alpha” from “beta”?

CAPM Model


\[ r = \alpha + \beta \, m \]

Basic Approach


  1. Generate random portfolios obeying risk limits
  2. Measure performance of random portfolios
  3. Compare actual with simulated returns

But what about insurance???

Steal the simple idea…

Use random portfolios of policies to do stuff

What sort of stuff?

Insurance Use Cases

Premium Forecasting


Lloyd’s Underwriter


Premium Planning


Knows the Market

Policy_Number Company_Sector Company_Name Premium Retention
GL00001 Technology Technology Co 2 $40,404 Medium
GL00002 Technology Technology Co 3 $41,952 Low
GL00005 Healthcare Healthcare Co 6 $32,854 Medium
GL00007 Construction Construction Co 8 $26,090 High
GL00008 Healthcare Healthcare Co 9 $25,467 Medium
GL00009 Renewable Energy Renewable Energy Co 10 $81,331 Medium
GL00012 Technology Technology Co 13 $37,076 High
GL00013 Renewable Energy Renewable Energy Co 14 $68,826 Low
GL00014 Renewable Energy Renewable Energy Co 15 $50,257 High
GL00015 Renewable Energy Renewable Energy Co 16 $34,535 High

Assigned High, Medium, Low chances of the retaining policy


Assign probability for policy


Run simulations

Premium Planning


US Liability Business


Grow from 60mm USD to 80mm USD

Where does the premium come from?

Northeast US -> 10mm


Heathcare sector -> 5mm


Small business -> 5mm

Co-occurrence of Risk Factors

Allocate by simulating policies


Also allocates across other policies

Portfolio Optimisation

Involved

Basic visualisations

Use pricing / loss models

Simulate portfolios

What does ‘optimal’ mean?

Proper use may require rethinking relationships

Summary


Random Portfolios are a powerful idea


Lots of use cases in insurance


Requires computational power

Thank You!


Slides for Talk


Detailed Work